Question

solve for x. round to the nearest tenth, if necessary.

answer attempt 1 out of 2

x =

Explanation:

Step1: Use the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 40^{\circ}\), the opposite side is \(RS = 35\), and the hypotenuse is \(x\). So, \(\sin40^{\circ}=\frac{35}{x}\).

Step2: Solve for \(x\)

Rearrange the equation \(\sin40^{\circ}=\frac{35}{x}\) to get \(x=\frac{35}{\sin40^{\circ}}\).
We know that \(\sin40^{\circ}\approx0.6428\). Then \(x=\frac{35}{0.6428}\approx54.5\).

Answer:

\(54.5\)